Question

If a 30 year bond with a face value of 1000 anda 5% coupon rate is selling for $947.51, which of the following could be the yield to maturity?

Assume a one year bond with a par value of $1000 and a coupon rate of 5%. What is the price if the current interest rate is 5%?

Answer 1

Q1) We need to understand that if the price is lower than the par value then the yield will be higher than the coupon rate

Next we need to solve the following equation:

Using a financial calculator or excel we can find out the value of r or the yield, which comes to 5.36% rounded to 2 decimal places

Year	CF	Discount Factor		Discounted CF
0	$              -	1/(1+0.0535540953114749)^0=	1	1*0=	-
1	$       50.00	1/(1+0.0535540953114749)^1=	0.949168158	0.949168157999859*50=	47.46
2	$       50.00	1/(1+0.0535540953114749)^2=	0.900920192	0.900920192160845*50=	45.05
3	$       50.00	1/(1+0.0535540953114749)^3=	0.855124759	0.855124759298187*50=	42.76
4	$       50.00	1/(1+0.0535540953114749)^4=	0.811657193	0.811657192643133*50=	40.58
5	$       50.00	1/(1+0.0535540953114749)^5=	0.770399162	0.770399162468419*50=	38.52
6	$       50.00	1/(1+0.0535540953114749)^6=	0.731238354	0.731238353964783*50=	36.56
7	$       50.00	1/(1+0.0535540953114749)^7=	0.694068161	0.694068161491602*50=	34.70
8	$       50.00	1/(1+0.0535540953114749)^8=	0.658787398	0.658787398369332*50=	32.94
9	$       50.00	1/(1+0.0535540953114749)^9=	0.625300021	0.625300021423738*50=	31.27
10	$       50.00	1/(1+0.0535540953114749)^10=	0.59351487	0.593514869532041*50=	29.68
11	$       50.00	1/(1+0.0535540953114749)^11=	0.563345415	0.563345415459254*50=	28.17
12	$       50.00	1/(1+0.0535540953114749)^12=	0.53470953	0.534709530309125*50=	26.74
13	$       50.00	1/(1+0.0535540953114749)^13=	0.50752926	0.507529259948482*50=	25.38
14	$       50.00	1/(1+0.0535540953114749)^14=	0.481730613	0.481730612796332*50=	24.09
15	$       50.00	1/(1+0.0535540953114749)^15=	0.457243358	0.457243358400038*50=	22.86
16	$       50.00	1/(1+0.0535540953114749)^16=	0.434000836	0.434000836250233*50=	21.70
17	$       50.00	1/(1+0.0535540953114749)^17=	0.411939774	0.411939774314032*50=	20.60
18	$       50.00	1/(1+0.0535540953114749)^18=	0.391000117	0.391000116792527*50=	19.55
19	$       50.00	1/(1+0.0535540953114749)^19=	0.371124861	0.371124860633693*50=	18.56
20	$       50.00	1/(1+0.0535540953114749)^20=	0.3522599	0.352259900355636*50=	17.61
21	$       50.00	1/(1+0.0535540953114749)^21=	0.334353881	0.334353880757773*50=	16.72
22	$       50.00	1/(1+0.0535540953114749)^22=	0.317358057	0.31735805711896*50=	15.87
23	$       50.00	1/(1+0.0535540953114749)^23=	0.301226163	0.301226162502017*50=	15.06
24	$       50.00	1/(1+0.0535540953114749)^24=	0.285914282	0.285914281803405*50=	14.30
25	$       50.00	1/(1+0.0535540953114749)^25=	0.271380732	0.271380732205191*50=	13.57
26	$       50.00	1/(1+0.0535540953114749)^26=	0.25758595	0.257585949703854*50=	12.88
27	$       50.00	1/(1+0.0535540953114749)^27=	0.244492381	0.244492381407051*50=	12.22
28	$       50.00	1/(1+0.0535540953114749)^28=	0.232064383	0.23206438330513*50=	11.60
29	$       50.00	1/(1+0.0535540953114749)^29=	0.220268123	0.220268123239103*50=	11.01
30	$       50.00	1/(1+0.0535540953114749)^30=	0.209071489	0.209071488800945*50=	10.45
30	$ 1,000.00	1/(1+0.0535540953114749)^30=	0.209071489	0.209071488800945*1000=	209.07
				PV= Sum of all Discounted CF	947.51

2)If the coupon rate = interest rate then the price is equal to the par value because: